#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgesdd_(char *jobz, integer *m, integer *n, real *a, integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt, real *work, integer *lwork, integer *iwork, integer *info ) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors. If singular vectors are desired, it uses a divide-and-conquer algorithm. The SVD is written A = U * SIGMA * transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A. Note that the routine returns VT = V**T, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= JOBZ (input) CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**T are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**T are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A; = 'N': no columns of U or rows of V**T are computed. M (input) INTEGER The number of rows of the input matrix A. M >= 0. N (input) INTEGER The number of columns of the input matrix A. N >= 0. A (input/output) REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**T (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). S (output) REAL array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). U (output) REAL array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M orthogonal matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. LDU (input) INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. VT (output) REAL array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. LDVT (input) INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N). WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK; LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1. If JOBZ = 'N', LWORK >= 3*min(M,N) + max(max(M,N),6*min(M,N)). If JOBZ = 'O', LWORK >= 3*min(M,N)*min(M,N) + max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). If JOBZ = 'S' or 'A' LWORK >= 3*min(M,N)*min(M,N) + max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)). For good performance, LWORK should generally be larger. If LWORK = -1 but other input arguments are legal, WORK(1) returns the optimal LWORK. IWORK (workspace) INTEGER array, dimension (8*min(M,N)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: SBDSDC did not converge, updating process failed. Further Details =============== Based on contributions by Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; static real c_b227 = 0.f; static real c_b248 = 1.f; /* System generated locals */ integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2, i__3; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__, ie, il, ir, iu, blk; static real dum[1], eps; static integer ivt, iscl; static real anrm; static integer idum[1], ierr, itau; extern logical lsame_(char *, char *); static integer chunk; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static integer minmn, wrkbl, itaup, itauq, mnthr; static logical wntqa; static integer nwork; static logical wntqn, wntqo, wntqs; static integer bdspac; extern /* Subroutine */ int sbdsdc_(char *, char *, integer *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *), sgebrd_(integer *, integer *, real *, integer *, real *, real *, real *, real *, real *, integer *, integer *); extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static real bignum; extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), sorgbr_(char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer * ); static integer ldwrkl; extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , real *, integer *, integer *); static integer ldwrkr, minwrk, ldwrku, maxwrk; extern /* Subroutine */ int sorglq_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); static integer ldwkvt; static real smlnum; static logical wntqas; extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); static logical lquery; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --s; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1; vt -= vt_offset; --work; --iwork; /* Function Body */ *info = 0; minmn = min(*m,*n); wntqa = lsame_(jobz, "A"); wntqs = lsame_(jobz, "S"); wntqas = wntqa || wntqs; wntqo = lsame_(jobz, "O"); wntqn = lsame_(jobz, "N"); lquery = *lwork == -1; if (! (wntqa || wntqs || wntqo || wntqn)) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < max(1,*m)) { *info = -5; } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < * m) { *info = -8; } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn || wntqo && *m >= *n && *ldvt < *n) { *info = -10; } /* Compute workspace (Note: Comments in the code beginning "Workspace:" describe the minimal amount of workspace needed at that point in the code, as well as the preferred amount for good performance. NB refers to the optimal block size for the immediately following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; if (*m >= *n && minmn > 0) { /* Compute space needed for SBDSDC */ mnthr = (integer) (minmn * 11.f / 6.f); if (wntqn) { bdspac = *n * 7; } else { bdspac = *n * 3 * *n + (*n << 2); } if (*m >= mnthr) { if (wntqn) { /* Path 1 (M much larger than N, JOBZ='N') */ wrkbl = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n; maxwrk = max(i__1,i__2); minwrk = bdspac + *n; } else if (wntqo) { /* Path 2 (M much larger than N, JOBZ='O') */ wrkbl = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "SORGQR", " ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + (*n << 1) * *n; minwrk = bdspac + (*n << 1) * *n + *n * 3; } else if (wntqs) { /* Path 3 (M much larger than N, JOBZ='S') */ wrkbl = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "SORGQR", " ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *n * *n; minwrk = bdspac + *n * *n + *n * 3; } else if (wntqa) { /* Path 4 (M much larger than N, JOBZ='A') */ wrkbl = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *m * ilaenv_(&c__1, "SORGQR", " ", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *n * *n; minwrk = bdspac + *n * *n + *n * 3; } } else { /* Path 5 (M at least N, but not much larger) */ wrkbl = *n * 3 + (*m + *n) * ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (wntqn) { /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; maxwrk = max(i__1,i__2); minwrk = *n * 3 + max(*m,bdspac); } else if (wntqo) { /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "QLN", m, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *m * *n; /* Computing MAX */ i__1 = *m, i__2 = *n * *n + bdspac; minwrk = *n * 3 + max(i__1,i__2); } else if (wntqs) { /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "QLN", m, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n * 3; maxwrk = max(i__1,i__2); minwrk = *n * 3 + max(*m,bdspac); } else if (wntqa) { /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = bdspac + *n * 3; maxwrk = max(i__1,i__2); minwrk = *n * 3 + max(*m,bdspac); } } } else if (minmn > 0) { /* Compute space needed for SBDSDC */ mnthr = (integer) (minmn * 11.f / 6.f); if (wntqn) { bdspac = *m * 7; } else { bdspac = *m * 3 * *m + (*m << 2); } if (*n >= mnthr) { if (wntqn) { /* Path 1t (N much larger than M, JOBZ='N') */ wrkbl = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m; maxwrk = max(i__1,i__2); minwrk = bdspac + *m; } else if (wntqo) { /* Path 2t (N much larger than M, JOBZ='O') */ wrkbl = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "SORGLQ", " ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + (*m << 1) * *m; minwrk = bdspac + (*m << 1) * *m + *m * 3; } else if (wntqs) { /* Path 3t (N much larger than M, JOBZ='S') */ wrkbl = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "SORGLQ", " ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *m * *m; minwrk = bdspac + *m * *m + *m * 3; } else if (wntqa) { /* Path 4t (N much larger than M, JOBZ='A') */ wrkbl = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *n * ilaenv_(&c__1, "SORGLQ", " ", n, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *m * *m; minwrk = bdspac + *m * *m + *m * 3; } } else { /* Path 5t (N greater than M, but not much larger) */ wrkbl = *m * 3 + (*m + *n) * ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (wntqn) { /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; maxwrk = max(i__1,i__2); minwrk = *m * 3 + max(*n,bdspac); } else if (wntqo) { /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", m, n, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; wrkbl = max(i__1,i__2); maxwrk = wrkbl + *m * *n; /* Computing MAX */ i__1 = *n, i__2 = *m * *m + bdspac; minwrk = *m * 3 + max(i__1,i__2); } else if (wntqs) { /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", m, n, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; maxwrk = max(i__1,i__2); minwrk = *m * 3 + max(*n,bdspac); } else if (wntqa) { /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR" , "PRT", n, n, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m * 3; maxwrk = max(i__1,i__2); minwrk = *m * 3 + max(*n,bdspac); } } } maxwrk = max(maxwrk,minwrk); work[1] = (real) maxwrk; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("SGESDD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = sqrt(slamch_("S")) / eps; bignum = 1.f / smlnum; /* Scale A if max element outside range [SMLNUM,BIGNUM] */ anrm = slange_("M", m, n, &a[a_offset], lda, dum); iscl = 0; if (anrm > 0.f && anrm < smlnum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & ierr); } else if (anrm > bignum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & ierr); } if (*m >= *n) { /* A has at least as many rows as columns. If A has sufficiently more rows than columns, first reduce using the QR decomposition (if sufficient workspace available) */ if (*m >= mnthr) { if (wntqn) { /* Path 1 (M much larger than N, JOBZ='N') No singular vectors to be computed */ itau = 1; nwork = itau + *n; /* Compute A=Q*R (Workspace: need 2*N, prefer N+N*NB) */ i__1 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Zero out below R */ i__1 = *n - 1; i__2 = *n - 1; slaset_("L", &i__1, &i__2, &c_b227, &c_b227, &a[a_dim1 + 2], lda); ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A (Workspace: need 4*N, prefer 3*N+2*N*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nwork = ie + *n; /* Perform bidiagonal SVD, computing singular values only (Workspace: need N+BDSPAC) */ sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 2 (M much larger than N, JOBZ = 'O') N left singular vectors to be overwritten on A and N right singular vectors to be computed in VT */ ir = 1; /* WORK(IR) is LDWRKR by N */ if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) { ldwrkr = *lda; } else { ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n; } itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__1 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy R to WORK(IR), zeroing out below it */ slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__1 = *n - 1; i__2 = *n - 1; slaset_("L", &i__1, &i__2, &c_b227, &c_b227, &work[ir + 1], & ldwrkr); /* Generate Q in A (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__1 = *lwork - nwork + 1; sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in VT, copying result to WORK(IR) (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* WORK(IU) is N by N */ iu = nwork; nwork = iu + *n * *n; /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in WORK(IU) and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+N*N+BDSPAC) */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite WORK(IU) by left singular vectors of R and VT by right singular vectors of R (Workspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &work[iu], n, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); /* Multiply Q in A by left singular vectors of R in WORK(IU), storing result in WORK(IR) and copying to A (Workspace: need 2*N*N, prefer N*N+M*N) */ i__1 = *m; i__2 = ldwrkr; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = min(i__3,ldwrkr); sgemm_("N", "N", &chunk, n, n, &c_b248, &a[i__ + a_dim1], lda, &work[iu], n, &c_b227, &work[ir], &ldwrkr); slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + a_dim1], lda); /* L10: */ } } else if (wntqs) { /* Path 3 (M much larger than N, JOBZ='S') N left singular vectors to be computed in U and N right singular vectors to be computed in VT */ ir = 1; /* WORK(IR) is N by N */ ldwrkr = *n; itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy R to WORK(IR), zeroing out below it */ slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__2 = *n - 1; i__1 = *n - 1; slaset_("L", &i__2, &i__1, &c_b227, &c_b227, &work[ir + 1], & ldwrkr); /* Generate Q in A (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagoal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+BDSPAC) */ sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of R and VT by right singular vectors of R (Workspace: need N*N+3*N, prefer N*N+2*N+N*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in A by left singular vectors of R in WORK(IR), storing result in U (Workspace: need N*N) */ slacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr); sgemm_("N", "N", m, n, n, &c_b248, &a[a_offset], lda, &work[ ir], &ldwrkr, &c_b227, &u[u_offset], ldu); } else if (wntqa) { /* Path 4 (M much larger than N, JOBZ='A') M left singular vectors to be computed in U and N right singular vectors to be computed in VT */ iu = 1; /* WORK(IU) is N by N */ ldwrku = *n; itau = iu + ldwrku * *n; nwork = itau + *n; /* Compute A=Q*R, copying result to U (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); /* Generate Q in U (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork], &i__2, &ierr); /* Produce R in A, zeroing out other entries */ i__2 = *n - 1; i__1 = *n - 1; slaset_("L", &i__2, &i__1, &c_b227, &c_b227, &a[a_dim1 + 2], lda); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in WORK(IU) and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+N*N+BDSPAC) */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite WORK(IU) by left singular vectors of R and VT by right singular vectors of R (Workspace: need N*N+3*N, prefer N*N+2*N+N*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in U by left singular vectors of R in WORK(IU), storing result in A (Workspace: need N*N) */ sgemm_("N", "N", m, n, n, &c_b248, &u[u_offset], ldu, &work[ iu], &ldwrku, &c_b227, &a[a_offset], lda); /* Copy left singular vectors of A from A to U */ slacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else { /* M .LT. MNTHR Path 5 (M at least N, but not much larger) Reduce to bidiagonal form without QR decomposition */ ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Perform bidiagonal SVD, only computing singular values (Workspace: need N+BDSPAC) */ sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { iu = nwork; if (*lwork >= *m * *n + *n * 3 + bdspac) { /* WORK( IU ) is M by N */ ldwrku = *m; nwork = iu + ldwrku * *n; slaset_("F", m, n, &c_b227, &c_b227, &work[iu], &ldwrku); } else { /* WORK( IU ) is N by N */ ldwrku = *n; nwork = iu + ldwrku * *n; /* WORK(IR) is LDWRKR by N */ ir = nwork; ldwrkr = (*lwork - *n * *n - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in WORK(IU) and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+N*N+BDSPAC) */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, & vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[ 1], info); /* Overwrite VT by right singular vectors of A (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); if (*lwork >= *m * *n + *n * 3 + bdspac) { /* Overwrite WORK(IU) by left singular vectors of A (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); /* Copy left singular vectors of A from WORK(IU) to A */ slacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda); } else { /* Generate Q in A (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */ i__2 = *lwork - nwork + 1; sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], & work[nwork], &i__2, &ierr); /* Multiply Q in A by left singular vectors of bidiagonal matrix in WORK(IU), storing result in WORK(IR) and copying to A (Workspace: need 2*N*N, prefer N*N+M*N) */ i__2 = *m; i__1 = ldwrkr; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = min(i__3,ldwrkr); sgemm_("N", "N", &chunk, n, n, &c_b248, &a[i__ + a_dim1], lda, &work[iu], &ldwrku, &c_b227, & work[ir], &ldwrkr); slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + a_dim1], lda); /* L20: */ } } } else if (wntqs) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+BDSPAC) */ slaset_("F", m, n, &c_b227, &c_b227, &u[u_offset], ldu); sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of A and VT by right singular vectors of A (Workspace: need 3*N, prefer 2*N+N*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else if (wntqa) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need N+BDSPAC) */ slaset_("F", m, m, &c_b227, &c_b227, &u[u_offset], ldu); sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Set the right corner of U to identity matrix */ if (*m > *n) { i__1 = *m - *n; i__2 = *m - *n; slaset_("F", &i__1, &i__2, &c_b227, &c_b248, &u[*n + 1 + ( *n + 1) * u_dim1], ldu); } /* Overwrite U by left singular vectors of A and VT by right singular vectors of A (Workspace: need N*N+2*N+M, prefer N*N+2*N+M*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } } } else { /* A has more columns than rows. If A has sufficiently more columns than rows, first reduce using the LQ decomposition (if sufficient workspace available) */ if (*n >= mnthr) { if (wntqn) { /* Path 1t (N much larger than M, JOBZ='N') No singular vectors to be computed */ itau = 1; nwork = itau + *m; /* Compute A=L*Q (Workspace: need 2*M, prefer M+M*NB) */ i__1 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Zero out above L */ i__1 = *m - 1; i__2 = *m - 1; slaset_("U", &i__1, &i__2, &c_b227, &c_b227, &a[(a_dim1 << 1) + 1], lda); ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A (Workspace: need 4*M, prefer 3*M+2*M*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nwork = ie + *m; /* Perform bidiagonal SVD, computing singular values only (Workspace: need M+BDSPAC) */ sbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 2t (N much larger than M, JOBZ='O') M right singular vectors to be overwritten on A and M left singular vectors to be computed in U */ ivt = 1; /* IVT is M by M */ il = ivt + *m * *m; if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) { /* WORK(IL) is M by N */ ldwrkl = *m; chunk = *n; } else { ldwrkl = *m; chunk = (*lwork - *m * *m) / *m; } itau = il + ldwrkl * *m; nwork = itau + *m; /* Compute A=L*Q (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__1 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy L to WORK(IL), zeroing about above it */ slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__1 = *m - 1; i__2 = *m - 1; slaset_("U", &i__1, &i__2, &c_b227, &c_b227, &work[il + ldwrkl], &ldwrkl); /* Generate Q in A (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__1 = *lwork - nwork + 1; sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U, and computing right singular vectors of bidiagonal matrix in WORK(IVT) (Workspace: need M+M*M+BDSPAC) */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], m, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of L and WORK(IVT) by right singular vectors of L (Workspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[ itaup], &work[ivt], m, &work[nwork], &i__1, &ierr); /* Multiply right singular vectors of L in WORK(IVT) by Q in A, storing result in WORK(IL) and copying to A (Workspace: need 2*M*M, prefer M*M+M*N) */ i__1 = *n; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = min(i__3,chunk); sgemm_("N", "N", m, &blk, m, &c_b248, &work[ivt], m, &a[ i__ * a_dim1 + 1], lda, &c_b227, &work[il], & ldwrkl); slacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1 + 1], lda); /* L30: */ } } else if (wntqs) { /* Path 3t (N much larger than M, JOBZ='S') M right singular vectors to be computed in VT and M left singular vectors to be computed in U */ il = 1; /* WORK(IL) is M by M */ ldwrkl = *m; itau = il + ldwrkl * *m; nwork = itau + *m; /* Compute A=L*Q (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy L to WORK(IL), zeroing out above it */ slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__2 = *m - 1; i__1 = *m - 1; slaset_("U", &i__2, &i__1, &c_b227, &c_b227, &work[il + ldwrkl], &ldwrkl); /* Generate Q in A (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IU), copying result to U (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need M+BDSPAC) */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of L and VT by right singular vectors of L (Workspace: need M*M+3*M, prefer M*M+2*M+M*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IL) by Q in A, storing result in VT (Workspace: need M*M) */ slacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl); sgemm_("N", "N", m, n, m, &c_b248, &work[il], &ldwrkl, &a[ a_offset], lda, &c_b227, &vt[vt_offset], ldvt); } else if (wntqa) { /* Path 4t (N much larger than M, JOBZ='A') N right singular vectors to be computed in VT and M left singular vectors to be computed in U */ ivt = 1; /* WORK(IVT) is M by M */ ldwkvt = *m; itau = ivt + ldwkvt * *m; nwork = itau + *m; /* Compute A=L*Q, copying result to VT (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Generate Q in VT (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[ nwork], &i__2, &ierr); /* Produce L in A, zeroing out other entries */ i__2 = *m - 1; i__1 = *m - 1; slaset_("U", &i__2, &i__1, &c_b227, &c_b227, &a[(a_dim1 << 1) + 1], lda); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in WORK(IVT) (Workspace: need M+M*M+BDSPAC) */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1] , info); /* Overwrite U by left singular vectors of L and WORK(IVT) by right singular vectors of L (Workspace: need M*M+3*M, prefer M*M+2*M+M*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IVT) by Q in VT, storing result in A (Workspace: need M*M) */ sgemm_("N", "N", m, n, m, &c_b248, &work[ivt], &ldwkvt, &vt[ vt_offset], ldvt, &c_b227, &a[a_offset], lda); /* Copy right singular vectors of A from A to VT */ slacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else { /* N .LT. MNTHR Path 5t (N greater than M, but not much larger) Reduce to bidiagonal form without LQ decomposition */ ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ i__2 = *lwork - nwork + 1; sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Perform bidiagonal SVD, only computing singular values (Workspace: need M+BDSPAC) */ sbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { ldwkvt = *m; ivt = nwork; if (*lwork >= *m * *n + *m * 3 + bdspac) { /* WORK( IVT ) is M by N */ slaset_("F", m, n, &c_b227, &c_b227, &work[ivt], &ldwkvt); nwork = ivt + ldwkvt * *n; } else { /* WORK( IVT ) is M by M */ nwork = ivt + ldwkvt * *m; il = nwork; /* WORK(IL) is M by CHUNK */ chunk = (*lwork - *m * *m - *m * 3) / *m; } /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in WORK(IVT) (Workspace: need M*M+BDSPAC) */ sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1] , info); /* Overwrite U by left singular vectors of A (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); if (*lwork >= *m * *n + *m * 3 + bdspac) { /* Overwrite WORK(IVT) by left singular vectors of A (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &ierr); /* Copy right singular vectors of A from WORK(IVT) to A */ slacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda); } else { /* Generate P**T in A (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */ i__2 = *lwork - nwork + 1; sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], & work[nwork], &i__2, &ierr); /* Multiply Q in A by right singular vectors of bidiagonal matrix in WORK(IVT), storing result in WORK(IL) and copying to A (Workspace: need 2*M*M, prefer M*M+M*N) */ i__2 = *n; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = min(i__3,chunk); sgemm_("N", "N", m, &blk, m, &c_b248, &work[ivt], & ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b227, & work[il], m); slacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 + 1], lda); /* L40: */ } } } else if (wntqs) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need M+BDSPAC) */ slaset_("F", m, n, &c_b227, &c_b227, &vt[vt_offset], ldvt); sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of A and VT by right singular vectors of A (Workspace: need 3*M, prefer 2*M+M*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else if (wntqa) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in U and computing right singular vectors of bidiagonal matrix in VT (Workspace: need M+BDSPAC) */ slaset_("F", n, n, &c_b227, &c_b227, &vt[vt_offset], ldvt); sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Set the right corner of VT to identity matrix */ if (*n > *m) { i__1 = *n - *m; i__2 = *n - *m; slaset_("F", &i__1, &i__2, &c_b227, &c_b248, &vt[*m + 1 + (*m + 1) * vt_dim1], ldvt); } /* Overwrite U by left singular vectors of A and VT by right singular vectors of A (Workspace: need 2*M+N, prefer 2*M+N*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } } } /* Undo scaling if necessary */ if (iscl == 1) { if (anrm > bignum) { slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (anrm < smlnum) { slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } } /* Return optimal workspace in WORK(1) */ work[1] = (real) maxwrk; return 0; /* End of SGESDD */ } /* sgesdd_ */